Max Alekseyev on Thu, 20 Nov 2008 00:29:34 +0100

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Pell's equations and beyond

Dear pari-users,

I dream about having the functionality of Dario Alpern's quadratic
bivariate Diophantine equation solver:
in PARI/GP. Is anything like that already present there?
At the moment, I'm not even sure if there is a simple way to solve
Pell's equations in PARI/GP.

Could you please clarify what is the best way (and if there exists one
without much programming) to solve the following equations in PARI/GP:

1) Pell's equation x^2 - D y^2 = 1, where D is integer ?

2) Generalized Pell's equation x^2 - D y^2 = c, where D and c are integer ?

3) Quadratic bivariate Diophantine equation in the general form: ax^2
+ bxy + cy^2 + dx + ey + f = 0, where a,b,c,d,e,f are integer
coefficients ?